Adaptive Variational Bayesian Cubature Quadrature Kalman Filter With Randomly Delayed Measurements and Unknown Noise Covariance Matrices

ABSTRACT This work presents a variational Bayesian (VB) adaptive quadrature Kalman filter, a new state estimation algorithm for nonlinear dynamic systems for a challenging situation where measurements face one‐step random delay and process as well as measurement noise covariance matrices remain unknown to the estimator. The random delay in the measurement is modeled as an independent Bernoulli random variable (BRV), and the proposed algorithm is subsequently formulated based on an exponential hierarchical Gaussian state‐space model of the likelihood function. In the absence of knowledge of the process and measurement noise covariances, the elements of predicted error covariance and measurement noise covariance are modeled using the inverse Wishart (IW) distribution which are jointly estimated along with the states with the newly designed VB‐based adaptive quadrature Kalman filter. The proposed algorithm is validated via simulation on a bearing‐only tracking (BoT) problem and a harmonic estimation problem using real‐time phase current data. Relative performance comparison of the proposed VB‐based algorithm with algorithms based on maximum likelihood estimation (MLE) and non‐adaptive approaches demonstrates the superiority of the proposed method. Furthermore, a comparative study of the VB‐based cubature quadrature Kalman filter (CQKF) against competing variants such as the unscented Kalman filter (UKF), cubature Kalman filter (CKF), and Gauss–Hermite filter (GHF) highlights the advantages of the proposed algorithm in terms of both performance and computational efficiency. The validation of the proposed algorithm with real measurements indicates the suitability of the proposed work for nonlinear state estimation.